Cacti Journey I

I'm back from my travels. I went to 3 states and 1 country so far this spring semester has been very emotional and eventful. In any case, I brought back some plants from my travels. The set are the Catci. The first cactus was the last cacti I got before I left.(I intentionally left the place out). It was so unique I had to have it. So I just snapped it off. The other cactus was the first one I got while in Cuba. I found it laying under a tree, shriveling it was returning back to dust. I sprinkled water on it. The healthier last three cacti I also got in Cuba. 

I am slightly nervous about whether or not they will live because of the difference in the weather. Cuba heat was bearable when I left in March, but I know temperatures can be scorching. I placed them under direct light (bulb). Then again I don't know I got a ton of hen's and chicks from NJ and they all died except one. Likewise a year ago while traveling, I brought back Jade plants which survived the winter but died the next summer. So, I'm taking special care. Instead of just using my potting soil. I've order Cacti soil from Amazon. I'm slightly hopeful as they seem sturdy.

 Two of them have already begun to sprout a new leaf. What is the next level of a cacti called? I know it can become its seperate plant, so I am excited about my two new baby cacti. The ends were already callous before I left Cuba, I just sprinkled water on them every day, finally adjusted one week later I am ready to plant!